The Pearson Product Moment Correlation Coefficient (r) measures the strength of the linear relationship between two variables. The r value is calculated using a formula involving the sum of the products of paired values and sum of squares for the two variables. r values range from +1 to -1, with values closer to these extremes indicating a stronger correlation and values closer to 0 indicating weaker or no correlation. A positive r represents a positive correlation and a negative r represents a negative correlation. The example calculates r = 0.962 for time spent studying and test scores, indicating a strong positive correlation.
1. Calculate the Pearson Product Moment Correlation Coefficient
2. Solve problems involving correlation analysis.
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1. Calculate the Pearson Product Moment Correlation Coefficient
2. Solve problems involving correlation analysis.
Visit the Website for more services it can offer: https://cristinamontenegro92.wixsite.com/onevs
This presentation covered the following topics:
1. Definition of Correlation and Regression
2. Meaning of Correlation and Regression
3. Types of Correlation and Regression
4. Karl Pearson's methods of correlation
5. Bivariate Grouped data method
6. Spearman's Rank correlation Method
7. Scattered diagram method
8. Interpretation of correlation coefficient
9. Lines of Regression
10. regression Equations
11. Difference between correlation and regression
12. Related examples
This slide describe the stepwise methods of hand calculation of Pearson correlation coefficient. it involves the hypothesis making and testing. Two methods are explained, one with covariance and second with direct formula. The formula derivation is also explained and at the last the graphic presentation is also given to show the line of fitness and direction of the correlation.
This session explains the alternative method of calculating correlation when variables are in ordinal forms. Spearman's correlation is applied between two ordinal or rank variables. The results are explained with the help of graph and critical tables.
Regression analysis is a mathematical measure of the average relationship between two or more variables in terms of the original units of the data.
In regression analysis there are two types of variables. The variable whose value is influenced or is to be predicted is called dependent variable and the variable which influences the values or is used for prediction, is called independent variable.
In regression analysis independent variable is also known as regressor or predictor or explanatory variable while the dependent variable is also known as regressed or explained variable.
This presentation covered the following topics:
1. Definition of Correlation and Regression
2. Meaning of Correlation and Regression
3. Types of Correlation and Regression
4. Karl Pearson's methods of correlation
5. Bivariate Grouped data method
6. Spearman's Rank correlation Method
7. Scattered diagram method
8. Interpretation of correlation coefficient
9. Lines of Regression
10. regression Equations
11. Difference between correlation and regression
12. Related examples
This slide describe the stepwise methods of hand calculation of Pearson correlation coefficient. it involves the hypothesis making and testing. Two methods are explained, one with covariance and second with direct formula. The formula derivation is also explained and at the last the graphic presentation is also given to show the line of fitness and direction of the correlation.
This session explains the alternative method of calculating correlation when variables are in ordinal forms. Spearman's correlation is applied between two ordinal or rank variables. The results are explained with the help of graph and critical tables.
Regression analysis is a mathematical measure of the average relationship between two or more variables in terms of the original units of the data.
In regression analysis there are two types of variables. The variable whose value is influenced or is to be predicted is called dependent variable and the variable which influences the values or is used for prediction, is called independent variable.
In regression analysis independent variable is also known as regressor or predictor or explanatory variable while the dependent variable is also known as regressed or explained variable.
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The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
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An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
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Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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The French Revolution Class 9 Study Material pdf free download
Module9 the pearson correlation
1. PEARSON PRODUCT MOMENT CORRELATION COEFFICIENT
The Pearson Product Moment Correlation Coefficient, denoted by 𝑟, measures the strength of the linear
relationship. To find the 𝑟, the following formula is used:
𝒓 =
𝒏(∑𝒙𝒚) − (∑ 𝒙)(∑ 𝒚)
√[𝒏(∑ 𝒙𝟐) − (∑ 𝒙)𝟐][𝒏(∑𝒚𝟐) − (∑ 𝒙)𝟐]
𝒏 = 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒑𝒂𝒊𝒓𝒆𝒅 𝒗𝒂𝒍𝒖𝒆𝒔
∑ 𝒙 = 𝒔𝒖𝒎 𝒐𝒇 𝒙 − 𝒗𝒂𝒍𝒖𝒆𝒔
∑ 𝒚 = 𝒔𝒖𝒎 𝒐𝒇 𝒚 − 𝒗𝒂𝒍𝒖𝒆𝒔
∑ 𝒙𝒚 = 𝒔𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒑𝒓𝒐𝒅𝒖𝒄𝒕𝒔 𝒐𝒇 𝒑𝒂𝒊𝒓𝒆𝒅 𝒗𝒂𝒍𝒖𝒆𝒔 𝒙 𝒂𝒏𝒅 𝒚
∑ 𝒙𝟐
= 𝒔𝒖𝒎 𝒐𝒇 𝒔𝒒𝒖𝒂𝒓𝒆𝒅 𝒙 − 𝒗𝒂𝒍𝒖𝒆𝒔
∑ 𝒚𝟐
= 𝒔𝒖𝒎 𝒐𝒇 𝒔𝒒𝒖𝒂𝒓𝒆𝒅 𝒚 − 𝒗𝒂𝒍𝒖𝒆𝒔
The following table below is the interpretation of 𝑟 and can be used in interpreting the degree of linear
relationship existing between the two variables.
Value of 𝒓 Strength of Correlation
+ 1.00 Perfect Positive Correlation
+ 0.71 to +0.99 Strong Positive Correlation
+ 0.51 to +0.70 Moderately Positive Correlation
+0.31 to +0.50 Weak Positive Correlation
+0.01 to +0.30 Negligible Positive Correlation
0 No Correlation
-0.01 to -0.30 Negligible Negative Correlation
-0.31 to -0.50 Weak Negative Correlation
-0.51 to -0.70 Moderately Negative Correlation
-0.71 to -0.99 Strong Negative Correlation
-1.00 Perfect Negative Correlation
EXAMPLE 1: The table below shows the time in hours per nigh studying (x) of six grade 11 students and
their scores on a statistics test (y). Solve for the Pearson Product Correlation Coefficient, 𝑟, and interpret
the result.
2. x 1 2 3 4 5 6
y 5 10 15 15 25 35
SOLUTION:
𝒙 𝒚 𝒙𝒚 𝒙𝟐
𝒚𝟐
1 5 5 1 25
2 10 20 4 100
3 15 45 9 225
4 15 60 16 225
5 25 125 25 625
6 35 210 36 1,225
∑ 𝒙 = 𝟐𝟏 ∑ 𝒚 = 𝟏𝟎𝟓 ∑ 𝒙𝒚 = 𝟒𝟔𝟓 ∑ 𝒙𝟐
= 𝟗𝟏 ∑ 𝒚𝟐
= 𝟐, 𝟒𝟐𝟓
𝒓 =
𝒏(∑𝒙𝒚) − (∑ 𝒙)(∑ 𝒚)
√[𝒏(∑ 𝒙𝟐) − (∑ 𝒙)𝟐][𝒏(∑𝒚𝟐) − (∑ 𝒙)𝟐]
𝒓 =
𝟔(𝟒𝟔𝟓) − (𝟐𝟏)(𝟏𝟎𝟓)
√[𝟔(𝟗𝟏) − (𝟐𝟏)𝟐][𝟔(𝟐, 𝟒𝟐𝟓) − (𝟏𝟎𝟓)𝟐]
=
𝟐, 𝟕𝟗𝟎 − 𝟐, 𝟐𝟎𝟓
√[𝟓𝟒𝟔 − 𝟒𝟒𝟏][𝟏𝟒, 𝟓𝟓𝟎 − 𝟏𝟏, 𝟎𝟐𝟓
𝒓 =
𝟓𝟖𝟓
√𝟑𝟕𝟎, 𝟏𝟐𝟓
= 𝟎. 𝟗𝟔𝟏𝟓𝟕 𝒐𝒓 𝟎. 𝟗𝟔𝟐
INTERPRETATION: The value 𝑟 = 0.962 is between +0.71 to +0.99 in the table for interpretation of 𝑟. It
indicates that there is a strong positive correlation between the time in hours spent in studying and the
scores test in statistics.
![PEARSON PRODUCT MOMENT CORRELATION COEFFICIENT
The Pearson Product Moment Correlation Coefficient, denoted by 𝑟, measures the strength of the linear
relationship. To find the 𝑟, the following formula is used:
𝒓 =
𝒏(∑𝒙𝒚) − (∑ 𝒙)(∑ 𝒚)
√[𝒏(∑ 𝒙𝟐) − (∑ 𝒙)𝟐][𝒏(∑𝒚𝟐) − (∑ 𝒙)𝟐]
𝒏 = 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒑𝒂𝒊𝒓𝒆𝒅 𝒗𝒂𝒍𝒖𝒆𝒔
∑ 𝒙 = 𝒔𝒖𝒎 𝒐𝒇 𝒙 − 𝒗𝒂𝒍𝒖𝒆𝒔
∑ 𝒚 = 𝒔𝒖𝒎 𝒐𝒇 𝒚 − 𝒗𝒂𝒍𝒖𝒆𝒔
∑ 𝒙𝒚 = 𝒔𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒑𝒓𝒐𝒅𝒖𝒄𝒕𝒔 𝒐𝒇 𝒑𝒂𝒊𝒓𝒆𝒅 𝒗𝒂𝒍𝒖𝒆𝒔 𝒙 𝒂𝒏𝒅 𝒚
∑ 𝒙𝟐
= 𝒔𝒖𝒎 𝒐𝒇 𝒔𝒒𝒖𝒂𝒓𝒆𝒅 𝒙 − 𝒗𝒂𝒍𝒖𝒆𝒔
∑ 𝒚𝟐
= 𝒔𝒖𝒎 𝒐𝒇 𝒔𝒒𝒖𝒂𝒓𝒆𝒅 𝒚 − 𝒗𝒂𝒍𝒖𝒆𝒔
The following table below is the interpretation of 𝑟 and can be used in interpreting the degree of linear
relationship existing between the two variables.
Value of 𝒓 Strength of Correlation
+ 1.00 Perfect Positive Correlation
+ 0.71 to +0.99 Strong Positive Correlation
+ 0.51 to +0.70 Moderately Positive Correlation
+0.31 to +0.50 Weak Positive Correlation
+0.01 to +0.30 Negligible Positive Correlation
0 No Correlation
-0.01 to -0.30 Negligible Negative Correlation
-0.31 to -0.50 Weak Negative Correlation
-0.51 to -0.70 Moderately Negative Correlation
-0.71 to -0.99 Strong Negative Correlation
-1.00 Perfect Negative Correlation
EXAMPLE 1: The table below shows the time in hours per nigh studying (x) of six grade 11 students and
their scores on a statistics test (y). Solve for the Pearson Product Correlation Coefficient, 𝑟, and interpret
the result.](https://image.slidesharecdn.com/module9thepearsoncorrelation-210220063047/85/Module9-the-pearson-correlation-1-320.jpg)
![x 1 2 3 4 5 6
y 5 10 15 15 25 35
SOLUTION:
𝒙 𝒚 𝒙𝒚 𝒙𝟐
𝒚𝟐
1 5 5 1 25
2 10 20 4 100
3 15 45 9 225
4 15 60 16 225
5 25 125 25 625
6 35 210 36 1,225
∑ 𝒙 = 𝟐𝟏 ∑ 𝒚 = 𝟏𝟎𝟓 ∑ 𝒙𝒚 = 𝟒𝟔𝟓 ∑ 𝒙𝟐
= 𝟗𝟏 ∑ 𝒚𝟐
= 𝟐, 𝟒𝟐𝟓
𝒓 =
𝒏(∑𝒙𝒚) − (∑ 𝒙)(∑ 𝒚)
√[𝒏(∑ 𝒙𝟐) − (∑ 𝒙)𝟐][𝒏(∑𝒚𝟐) − (∑ 𝒙)𝟐]
𝒓 =
𝟔(𝟒𝟔𝟓) − (𝟐𝟏)(𝟏𝟎𝟓)
√[𝟔(𝟗𝟏) − (𝟐𝟏)𝟐][𝟔(𝟐, 𝟒𝟐𝟓) − (𝟏𝟎𝟓)𝟐]
=
𝟐, 𝟕𝟗𝟎 − 𝟐, 𝟐𝟎𝟓
√[𝟓𝟒𝟔 − 𝟒𝟒𝟏][𝟏𝟒, 𝟓𝟓𝟎 − 𝟏𝟏, 𝟎𝟐𝟓
𝒓 =
𝟓𝟖𝟓
√𝟑𝟕𝟎, 𝟏𝟐𝟓
= 𝟎. 𝟗𝟔𝟏𝟓𝟕 𝒐𝒓 𝟎. 𝟗𝟔𝟐
INTERPRETATION: The value 𝑟 = 0.962 is between +0.71 to +0.99 in the table for interpretation of 𝑟. It
indicates that there is a strong positive correlation between the time in hours spent in studying and the
scores test in statistics.](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)